# 自定义相关性函数
## Correlation matrix with p-values. See http://goo.gl/nahmV for documentation of this function
cor.prob <- function (X, dfr = nrow(X) - 2) {
  R <- cor(X, use="pairwise.complete.obs")
  above <- row(R) < col(R)
  r2 <- R[above]^2
  Fstat <- r2 * dfr/(1 - r2)
  R[above] <- 1 - pf(Fstat, 1, dfr)
  R[row(R) == col(R)] <- NA
  R
}

## Use this to dump the cor.prob output to a 4 column matrix
## with row/column indices, correlation, and p-value.
## See StackOverflow question: http://goo.gl/fCUcQ
flattenSquareMatrix <- function(m) {
  if( (class(m) != "matrix") | (nrow(m) != ncol(m))) stop("Must be a square matrix.") 
  if(!identical(rownames(m), colnames(m))) stop("Row and column names must be equal.")
  ut <- upper.tri(m)
  data.frame(i = rownames(m)[row(m)[ut]],
             j = rownames(m)[col(m)[ut]],
             cor=t(m)[ut],
             p=m[ut])
}